I have read in the paper of Meigniez "Submersions, fibrations and bundles" that a smooth surjective submersion $f: E \rightarrow B$ whose fibers are all diffeomorphic to $\mathbb{R}^{n}$ is locally trivial, i.e. a fiber bundle (corollay 31).

1. Is there a counterexample for $f$ not a submersion, which is not a fiber bundle even topologically?

2. Is there a smooth family of vector spaces all isomorphic to $\mathbb{R}^{n}$ which is not a vector bundle, even topologically?